Bi-modal catheter steering mechanism

ABSTRACT

Medical devices, systems, and methods for treating patients with tissue ablation include catheter systems having bi-modal steering mechanisms, which are capable of both linear and loop ablation. In other words, the catheter system may have two different steering modes: two-dimensional and three-dimensional. In the first and second steering modes, the steering actuator may cause one or more portions of the catheter shaft to bend in different planes. A steerable ablation catheter may include treatment elements such as electrodes at its distal end and along the catheter shaft, each of which may map, pace, and ablate.

CROSS-REFERENCE TO RELATED APPLICATION

Not applicable.

STATEMENT REGARDING FEDERALLY SPONSORED RESEARCH OR DEVELOPMENT

Not applicable.

FIELD OF THE INVENTION

The present invention relates generally to medical devices, and more particularly to steerable catheters, systems, and methods for treating patients through ablation of tissue.

BACKGROUND OF THE INVENTION

Numerous procedures involving catheters and other minimally invasive devices may be performed to provide a wide variety of medical treatments, such as ablation, angioplasty, dilation and others. The term “atrial fibrillation” is a type of cardiac arrhythmia, or irregular heartbeat, in which the atria fail to contract effectively. Normal sinus rhythm of the heart begins with an electrical impulse generated by the sinus node that propagates across the right and left atria (the two small upper chambers of the heart) to the atrioventricular node. Atrial contraction leads to pumping blood into the ventricles in synchronization with the electrical pulse.

During atrial fibrillation, disorganized electrical conduction in the atria causes rapid uncoordinated contractions, resulting in sub-optimal pumping of blood into the ventricle. The atrioventricular node may receive sporadic electrical impulses from many locations throughout the atria, instead of only from the sinus node. This electrical confusion may overwhelm the atrioventricular node, producing an irregular and rapid heartbeat. Consequently, blood may pool in the atria and increase a risk for blood clots.

While there are numerous variations of atrial fibrillation with different causes, they all involve irregularities in the transmission of electrical impulses through the heart. As a result, the heart does not pump the blood properly, and it may pool and clot. If a blood clot forms and moves to an artery in the brain, atrial fibrillation can lead to stroke.

The major risk factors for atrial fibrillation include age, coronary artery disease, rheumatic heart disease, hypertension, diabetes, and thyrotoxicosis. Atrial fibrillation affects 7% of the population over 65 years of age, and is also associated with increased risks of congestive heart failure and cardiomyopathy, which warrant medical attention and treatment. Atrial fibrillation is the most common sustained heart rhythm disorder and increases the risk for heart disease and stroke, both leading causes of death in the United States.

To treat cardiac arrhythmias including atrial fibrillation, physicians often employ specialized ablation catheters to gain access into interior regions of the body. Such catheters often include tip electrodes or other ablating elements used to create ablation lesions that physiologically alter the ablated tissue without removal thereof, and thereby disrupt or block electrical pathways through the targeted tissue.

In the treatment of cardiac arrhythmias, a specific area of cardiac tissue having aberrant electrically conductive pathways, such as atrial rotors, emitting or conducting erratic electrical impulses, may be initially localized. A physician may direct a catheter through a main vein or artery into the interior region of the heart that is to be treated. The ablating portion of the selected device is next placed near the targeted cardiac tissue that is to be ablated, such as a pulmonary vein ostium or atrium.

An ablation procedure may involve creating a series of inter-connecting lesions, to electrically isolate tissue believed to be the source of an arrhythmia. During such a procedure, a physician may employ several different catheters having variations in geometry and dimensions of the ablative element in order to produce the desired ablation pattern. Multiple devices having varying dimensions and shapes may also be used, to account for variations in anatomy. Each catheter may have a unique geometry for creating a specific lesion pattern or size, with the multiple catheters being sequentially removed and replaced to create the desired multiple lesions.

For example, some catheters may be capable of following a two-dimensional curve, which may be referred to as “curvilinear” or “linear” ablation. Other catheters may be capable of forming a three-dimensional shape, such as a loop that is almost transverse to the catheter's longitudinal axis, which may be referred to as “loop” ablation.

Accordingly, it is desirable to provide a single medical device capable of both linear and loop ablation, thereby reducing the need for additional medical devices.

SUMMARY OF THE INVENTION

The present invention advantageously provides medical devices, systems, and methods for treating patients with tissue ablation. In particular, catheter systems are provided having bi-modal steering mechanisms, which are capable of both linear and loop ablation. The catheter system may have two different steering modes: two-dimensional and three-dimensional. In the first and second steering modes, the steering actuator may cause one or more portions of the catheter shaft to bend in different planes. A steerable ablation catheter may include treatment elements such as electrodes at its distal end and along the catheter shaft, each of which may map, pace, and ablate. Optional features include a series of thermocouples for monitoring local temperatures.

Methods for ablating a tissue region are also provided, including directing a treatment assembly of a medical device toward a tissue region, and the treatment element may include a series or an array of electrodes; selecting a first or second steering mode; in the first steering mode, manipulating a steering actuator from an initial position to cause a first portion of the catheter body to bend from an initial shape to a first arc shape along a first plane; in the second steering mode, manipulating the steering actuator from the initial position to cause the first portion to bend from the initial shape to a second arc shape, and to cause a second portion of the catheter body to bend along a second plane; and delivering ablative energy to the treatment assembly. The method may also include monitoring an electrical signal of the tissue region, such as a cardiac tissue region, or monitoring temperatures of the electrodes.

A medical device is also provided, having a catheter body defining a proximal portion and a distal portion; a steering actuator coupled to the proximal portion of the catheter body; a first steering element having a first end attached to the steering actuator and a second end attached to the distal portion of the catheter body; a second steering element having a first end attached to the steering actuator and a second end attached to the catheter body distal to the first steering element; and an electrode array disposed on the distal end of the catheter body. The first steering element may be attached to a first side of the distal portion, and the second steering actuator may be attached to a second side opposite the first side of the distal portion, such that manipulation of the steering actuator in a first direction tensions the first steering element to deflect a portion of the catheter body in a first direction in a first plane and manipulation of the steering actuator in a second direction tensions the second steering element to deflect a portion of the catheter body in a second direction in a first plane. The catheter body may include a first deflectable segment proximal to the electrode array, the first deflectable segment being biased to deflect in a plane substantially perpendicular to the first plane. A stiffener element may be slidably disposed within the catheter body and slidably positionable within the first deflectable segment. The medical device may include a first anchoring element circumscribing the catheter body where the first steering element attaches to the distal portion; and a second anchoring element circumscribing the catheter body where the second steering element attaches to the distal portion.

A medical device having a catheter body; a guide member within the catheter body, the guide member defining a first segment having a first plane of preferential bending, and a second segment having a second plane of preferential bending substantially perpendicular to the first plane; a first steering element having a first end attached to the first segment of the guide member; a second steering element having a first end attached to the second segment of the guide member; and an electrode array disposed on the distal end of the catheter body is also provided, and may also include a first steering actuator coupled to the first steering element, and a second steering actuator coupled to the second steering element, where manipulation of the first steering actuator tensions the first steering element to deflect a portion of the catheter body in the first plane, and wherein manipulation of the second steering actuator tensions the second steering element to deflect a portion of the catheter body in the second plane.

A more complete understanding of the present invention, and its associated advantages and features, will be more readily understood by reference to the following description and claims, when considered in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

In this description, reference will be made to the attached drawings:

FIG. 1 is a side elevation view of a first catheter embodiment;

FIG. 2 is a partial cross-section view of the catheter shaft of FIG. 1, showing different steering modes;

FIGS. 2A-2C are partial perspective views of a catheter, showing loop steering;

FIG. 3 is a partial cut-away view of a catheter, showing loop steering;

FIGS. 4 and 5 are partial perspective views of a guide plate;

FIGS. 6 and 7 are partial perspective views of additional guide plates;

FIG. 8 is a side elevation view of a second catheter embodiment;

FIGS. 9 and 10 are partial views, showing different positions of a stiffening wire;

FIGS. 11A-12C are partial cross-section views of the catheter of FIG. 8, showing different steering modes;

FIGS. 13A and 13B are partial cross-section views of the catheter shaft of FIG. 8;

FIGS. 14A-15 are partial views of catheters, showing loop steering;

FIGS. 16 and 17 are side elevation views of a third and fourth catheter embodiment;

FIGS. 18 and 19 are partially diagrammatic views of catheters having thermocouples; and

FIG. 20 is a partial view some catheter components.

DETAILED DESCRIPTION OF THE INVENTION

The present invention advantageously provides medical devices, systems, and methods for treating patients, in particular with catheter systems having bi-modal steering mechanisms, which are capable of both linear and loop ablation.

Referring to the drawings, the present invention provides various embodiments of medical devices for treating patients, which may be in the form of catheters having more than one steering mode. The illustrations of course depict only some of many different possible catheter designs that are within the scope of the present invention. For clarity and convenience, the present detailed description will only describe a few embodiments.

The catheters of the present invention may be sized and dimensioned for intraluminal and transseptal access to a patient's heart for the treatment or ablation thereof. Some of these embodiments are in the form of catheters generally designated at reference numerals 10 and 12, and catheter shaft designs generally designated at reference numerals 14 and 16.

A first example embodiment of the present invention is shown in FIG. 1. Medical device 10 may generally define an elongated, flexible catheter body 18 with proximal and distal ends having a distal treatment assembly 20 that may include a series of electrodes 22, as well as a handle assembly 24 at a proximal end or portion of the catheter body 18. The catheter body 18 may be formed and dimensioned to provide sufficient column and torsional strength to support standard interventional procedures such as those which access the vasculature from a femoral vein or artery and further access the patient's heart. The catheter shaft may include reinforcement elements or otherwise be constructed to provide desired degrees of stiffness, flexibility, and torque transmission along the length of the body and at selected locations along its length. For example, the catheter body may have portions or components of differing size, thickness or flexibility, and may include wires, braiding, changes in wall thickness, additional wall layers or catheter body components, sleeves, or other components reinforcing or otherwise supplementing an outer wall or thickness along its length. Some portions that may experience significant loading or torque during a particular procedure may also include reinforcement.

FIG. 1 depicts medical device 10 having a handle assembly 24 with a knob or steering actuator 28. Steering actuator 28 may have an initial or neutral position, and may be moved in one direction to a first position, and in another direction to a second position. The catheter shaft may have portions of relatively higher and lower flexibility, and may have a proximal portion of a larger size than a distal portion.

The catheter shaft design of this first example embodiment is shown in FIG. 2. A first and second steering member or wire 34 and 36 are depicted, affixed to radially or diametrically opposite sides of the catheter body 18. First and second steering wires 34 and 36 have proximal ends coupled to steering actuator 28 for selectively pulling either steering wire. The steering wires 34 and 36 are generally free from attachment to other catheter components up to a first and second attachment point 38 and 40, which are at different longitudinal positions. These different attachment points enable the same steering actuator 28 to select and operate the catheter in a first steering mode by twisting or moving steering actuator 28 in a first direction, and to select and operate the catheter in a second steering mode by twisting or moving steering actuator 28 in a second direction. Accordingly, a single steering actuator 28 can provide two different steering modes, either two-dimensional or three-dimensional.

The catheter body may also have at least four portions of alternating higher and lower flexibility 52, 54, 56 and 58. The distal portion of higher flexibility 52 may encompass the treatment assembly 20, for example including all of the electrodes 22, and this portion may be what bends to form the curved shape of the two-dimensional steering mode, and to form the loop of the three-dimensional steering mode. The proximal portion of higher flexibility 56 may encompass bending in the three-dimensional steering mode, to create the desired angle of the loop with respect to the longitudinal axis. In a specific example, the portions of higher flexibility may be polymers having durometers of 30-40 D, and the portions of lower flexibility may be polymers having durometers of 50-60 D.

The catheters of the present invention may have a proximal and distal plane of preferential bending. This compound preferential bending may be achieved with a guide plate 64 as shown in FIGS. 3-5, having proximal and distal portions 66 and 68 and a transition portion 70. Transition portion 70 may have the illustrated twisted shape, and the angle may be selected as desired, which may for example be 90 degrees. The proximal portion 66 of guide plate may optionally have a curved or concave section 71, which may be provided to bias the catheter shaft during the three-dimensional steering mode. Additional possible designs for guide plates are shown in FIGS. 6 and 7.

In operation, the steering actuator 28 may initially be in a neutral position, and the distal catheter shaft will be generally straight (with the possible exception of a curved or concave section 71 of a guide plate), though it will of course tend to follow the shape of any body passage or lumen. FIG. 1 illustrates the treatment assembly 20 as generally following an x-axis. For linear ablation, or at any time two-dimensional steering is desired according to the first steering mode, the steering actuator 28 may be moved or rotated in a first direction to a first position, thus pulling on first steering member 34 and causing distal portion 68 of guide plate 64 inside the catheter body's distal portion of higher flexibility 52 to bend in the distal plane of preferential bending. This bending may be toward the y-axis of FIG. 1, into a shape illustrated in FIG. 2A. In the two-dimensional steering mode, the term “linear” of course includes curving lines, as shown in FIG. 2A.

For loop ablation, or at any time three-dimensional steering is desired according to the second steering mode, the steering actuator 28 may be moved or rotated in a second direction to a second position, thus pulling on second steering member 36. In this second steering mode, distal portion 68 of guide plate 64 inside the catheter body's distal portion of higher flexibility 52 will bend in the distal plane of preferential bending, but in the opposite direction as illustrated in FIGS. 2B and 2C. Simultaneously, proximal portion 66 of guide plate 64 inside the catheter body's proximal portion of higher flexibility 56 will bend in the proximal plane of preferential bending.

In this three-dimensional steering mode, a distal portion of catheter body may be formed into a loop as shown in FIGS. 2B and 2C, and a more proximal portion of catheter body may bend toward the z-axis of FIG. 1, such that the loop defines an angle with respect to the longitudinal axis of an adjacent portion of catheter body. This angle may have whatever magnitude the physician prefers, including 90 degrees. An angle somewhat less than perpendicular may be selected, to provide a measure of resilience or tactile feedback when contacting tissue.

Another example embodiment of a medical device according to the present invention is shown in FIG. 8, having a bi-directional shaft design with a discrete mechanism for selecting between different steering modes. Catheter 12 is generally similar to catheter 10 with a handle assembly 26 having a steering knob or actuator 30 as well as an additional controller, such as for example slider 32, and a different catheter shaft design 16.

This mechanism for selecting different steering modes may be in the form of a movable stiffener 48, shown in FIGS. 9-12C. The stiffener 48 may be moved to the distal position of FIGS. 9 and 11A-11C, selecting a first mode of steering, or to the proximal position of FIGS. 10 and 12A-12C, thus selecting a second steering mode. In the first steering mode of FIGS. 9 and 11A-11C, stiffener 48 may oppose bending of the proximal portion 66 of the guide plate 64, which may be referred to as two-dimensional or “linear” steering. On the other hand, in the second steering mode of FIGS. 10 and 12A-12C, stiffener 48 is retracted proximally and allows bending of the proximal portion 66 of the guide plate 64 (toward the z-axis for example), which may be referred to as three-dimensional or “loop” steering.

The catheter shaft design of this second example embodiment is shown in FIGS. 13A and 13B, depicting another pair of first and second steering wires 42 and 44, affixed to radially or diametrically opposite sides of the catheter body at the same longitudinal position 46. First and second steering wires 42 and 44 have proximal ends coupled to steering knob 30 for selectively pulling either steering wire. The steering wires 42 and 44 are generally free from attachment to other catheter components up to attachment points 46. With both of the steering wires 42 and 44 acting on the same longitudinal position, the steering actuator 30 is operable to bend the catheter shaft in a first and second direction by twisting or moving the steering actuator in a first and second direction, respectively, in both a first and second steering mode.

In embodiments having the bi-directional shaft design, the stiffener 48 is coupled at its proximal end with a controller, such as for example slider 32 shown in FIG. 8, which is operable to move stiffener between the distal position of FIGS. 9 and 11A-11C and the proximal position of FIGS. 10 and 12A-12C. This bi-directional shaft design also allows hybrid steering modes: by moving the stiffener 48 to intermediate positions between the proximal and distal positions, combinations of the first and second steering modes may be achieved.

Additional optional components for catheter shafts according to the present invention may include reinforcements such as for example a braid or coil embedded in or affixed to the catheter body, which may be made of any suitable material including metals and strong polymers. Specific examples of reinforcing materials may include stainless steel and nitinol. These reinforcing components may also be used to more strongly affix the steering wires to the catheter body, such as for example by embedding them into the wall of catheter body, inside or outside of (or even woven among) reinforcing components. FIG. 15 also illustrates optional anchoring components, which may include a first and second anchoring ring 60 and 62, and which may be used to affix the steering wires to the catheter body.

Another example embodiment of a medical device according to the present invention is shown in FIG. 16, having a supplemental steering mechanism for more agile manipulation of the distal assembly. Catheter 76 has a handle assembly 78 having a first and second steering knob or actuator 80 and 82. First steering actuator 80 may be generally similar to steering actuator 28 of catheter 10, or may be generally similar to steering actuator 30 of catheter 12 with the addition of optional slider 84 for controlling a stiffener.

Second steering actuator 82 may be used to bend and steer a more proximal portion of the catheter shaft, to more deftly position the distal assembly near a desired site of tissue for treatment. In catheter shaft designs having at least four alternating portions of higher and lower flexibility, the second steering actuator 82 may enable bending and steering of a supplemental steering portion, which is proximal of the proximal portion of higher flexibility.

Another example embodiment of a medical device according to the present invention is shown in FIG. 17, having a supplemental steering mechanism in the form of a steerable catheter sheath 86, which at least partially surrounds an ablation catheter 88 according to the present invention. Catheter 88 has a handle assembly 90 having a steering knob or actuator 92, and may have an optional slider 94. Catheter sheath 86 has a handle assembly 96 with a sheath steering knob or actuator 98. Catheter 88 and catheter sheath 86 may be moved, more specifically advanced, retracted or rotated, with respect to each other. The sheath steering actuator 98 may be used to bend and steer a selected portion of the catheter shaft, and sheath 86 may be moved so as to steer different portions of the catheter shaft.

Now referring to FIGS. 18 and 19, the distal treatment assembly 20 provides for the treatment, monitoring, or otherwise clinically interacting with a desired tissue region, such as the heart. The treatment assembly 20 may include, for example, an array or series of electrodes 22 disposed near, on, or substantially on the distal end of the catheter body. The electrodes 22 may be mounted to detect electrical signals between any pair of electrodes (bi-pole) for mapping of electrical activity, and/or for performing other functions such as pacing of the heart. Moreover, the electrodes 22 may deliver ablation energy across an electrode pair or from independent electrodes when delivering monopolar energy. In a particular example, the plurality of electrodes may include from eight to twelve electrodes, with either symmetric or asymmetric spacing. The electrodes 22 may be constructed from platinum, iridium, or any other suitable material.

Each electrode 22 may include a temperature sensor or thermocouple 72 located on or near the tissue side of the electrode, to monitor the temperature at each ablation site before and during ablation. Indeed, each electrode 28 may have a pair of thermocouples at radially or diametrically opposite points. The thermocouples are electrically connected to the handle assembly by conduits or wires, which may optionally be at least partially surrounded by a coil 74 shown in FIG. 20 to improve signal fidelity. To reduce the quantity of thermocouples and associated wires, a smaller number of thermocouples may be used and arranged specifically to still provide good performance. For example, a quantity of the temperature sensors is at least equal to a quantity of the electrodes, and is at most twice the quantity of electrodes. A more detailed example includes at least eight electrodes, and at most twelve temperature sensors. In the specific examples depicted in FIGS. 18 and 19, ten electrodes and twelve thermocouples are depicted. The thermocouples shown in FIG. 18 are arranged generally on one radial side of the catheter body, with two thermocouples on the radially opposite side of the catheter body. In FIG. 19, the thermocouples are positioned on alternating radially opposite sides of the catheter body.

It should be understood that an unlimited number of configurations for the present invention could be realized. The foregoing discussion describes merely exemplary embodiments illustrating the principles of the present invention, the scope of which is recited in the following claims. In addition, unless otherwise stated, all of the accompanying drawings are not to scale. Those skilled in the art will readily recognize from the description, claims, and drawings that numerous changes and modifications can be made without departing from the spirit and scope of the invention. 

What is claimed is:
 1. A medical device, comprising: a catheter body defining a proximal portion and a distal portion, the distal portion including a plurality of adjacent segments having alternating relative flexibilities; a guide member within the catheter body, the guide member defining a first outer edge, a second outer edge, a longitudinal axis, a width that is perpendicular to the longitudinal axis and extends directly from the first outer edge of the guide member directly to the second outer edge of the guide member, a length that is located along the longitudinal axis, a first segment having a first plane of preferential bending, a second segment having a second plane of preferential bending substantially perpendicular to the first plane of preferential bending, and a transition portion between the first segment and the second segment, the first segment having a distal section, a proximal section, and a middle section located directly between the distal section and the proximal section, the middle section having a width that extends directly from the first outer edge of the guide member directly to the second outer edge of the guide member, the distal section and the proximal section being linear and located along the guide member longitudinal axis and an entirety of the middle section having an arc of curvature when the guide member is in an at least substantially linear configuration; a steering actuator coupled to the proximal portion of the catheter body; a first steering element having a first end attached to the steering actuator and a second end attached to the distal portion of the catheter body at a first position; a second steering element having a first end attached to the steering actuator and a second end attached to the catheter body at a second position distal to the first position; and an electrode array disposed on the distal portion of the catheter body.
 2. The medical device according to claim 1, wherein the first steering element is attached to a first side of the distal portion, and the second steering element is attached to a second side of the distal portion opposite the first side of the distal portion.
 3. The medical device according to claim 1, wherein the steering actuator is configured to provide tension to the first steering element to deflect a portion of the catheter body in a first direction in a first plane when the steering actuator is manipulated in a first direction.
 4. The medical device according to claim 3, wherein the steering actuator is configured to provide tension to the second steering element to deflect the portion of the catheter body in a second direction in a second plane when the steering actuator is manipulated in a second direction.
 5. The medical device according to claim 1, further comprising a first anchoring element at the first position; and a second anchoring element at the second position.
 6. The medical device according to claim 1, wherein the first and second steering elements are steering wires.
 7. The medical device according to claim 1, wherein the steering elements are attached to the catheter body at the same longitudinal position.
 8. A medical device, comprising: a catheter body; a guide member within the catheter body, the guide member defining a width, a first outer edge, a second outer edge, a longitudinal axis, a width that extends directly from the first outer edge directly to the second outer edge, a length that is located along the longitudinal axis, a first segment having a first plane of preferential bending, a second segment having a second plane of preferential bending substantially perpendicular to the first plane, and a transition portion between the first segment and the second segment, the first segment having a distal section, a proximal section, and a middle section located directly between the distal section and the proximal section, the middle section having a width that extends directly from the first outer edge of the guide member and directly to the second outer edge of the guide member, the distal section and the proximal section being located along the guide member longitudinal axis and an entirety of the middle section having an arc of curvature when the guide member is in an at least substantially linear configuration; a first and second steering element, each of the first and the second steering elements having an end attached to the catheter body at a position proximal of the first segment; and an electrode array disposed on a distal portion of the catheter body.
 9. The medical device according to claim 8, further comprising a steering actuator coupled to the first and second steering elements.
 10. The medical device according to claim 9, wherein the first and second steering elements are attached to the catheter body at different longitudinal positions, wherein the steering actuator is configured to provide tension to the first steering element to deflect the first segment in a first direction in the first plane when the steering actuator is manipulated in a first direction, and wherein the steering actuator is configured to provide tension to the second steering element to deflect the second segment in a second direction in the second plane when the steering actuator is manipulated in a second direction.
 11. The medical device according to claim 9, further comprising: a sheath at least partially surrounding a portion of the catheter body; and a sheath steering actuator coupled to the sheath, wherein manipulation of the sheath steering actuator deflects a portion of the sheath.
 12. A medical device, comprising: a catheter body; a guide member within the catheter body, the guide member defining a first outer edge, a second outer edge, a longitudinal axis, a width that extends directly from the first outer edge directly to the second outer edge, a first segment having a first plane of preferential bending, a second segment having a second plane of preferential bending, and a transition portion between the first segment and the second segment, the first segment having a distal section, a proximal section, and a middle section located directly between the distal section and the proximal section, the middle section having a width that extends directly from the first outer edge of the guide member and directly to the second outer edge of the guide member, the distal section and the proximal section being located along the guide member longitudinal axis and an entirety of the middle section having an arc of curvature when the guide member is in an at least substantially linear configuration; a first steering element and a second steering element, each of the first and second steering elements having an end attached to the catheter body; a steering actuator coupled to the first and the second steering elements, the steering actuator being configured to provide tension to the first and the second steering elements when the steering actuator is manipulated in a first direction and a second direction, respectively; and an electrode. 